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I am not sure he invented it; but the imaginary numbers were first invented to solve equations with third-degree and fourth-degree polynomials. They were at first considered an artifact to solve those problems, with no real meaning - hence the historical name "imaginary".

Nowadays it is known that complex numbers (that consist of a real and an imaginary part) have lots of applications; to name only a few: electricity; quantum mechanics; art (ever seen a fractal, like the Mandelbrot set?).

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Q: Why did Carl Friedrich Gauss invent the imaginary number?
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